Related papers: Some remarks on Mathieu subspaces over associative…
We review our recent formulation of Colombeau type algebras as Hausdorff sequence spaces with ultranorms, defined by sequences of exponential weights. We extend previous results and give new perspectives related to echelon type spaces,…
We introduce a class of locally compact Hausdorff groupoids and show how to associate C*-algebras to them in a way which generalizes the reduced C*-algebra of an 'etale groupoid. Focusing on criteria for simplicity and existence of Cartan…
We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations. We…
We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).
In this paper, we collect basic properties of the Albanese dimension and explain how to generalize the main theorem of [F2](math.AG/0204262). This paper is a supplement and a generalization of [F2]. We also prove an inequality of…
In this book, the authors define several new types of soft neutrosophic algebraic structures over neutrosophic algebraic structures and we study their generalizations. These soft neutrosophic algebraic structures are basically parameterized…
We look at classes of semiassociative algebras, with an emphasis on those that canonically generalize associative (generalized) cyclic algebras, and at their behaviour in the semiassociative Brauer monoid defined by Blachar, Haile, Matzri,…
The present paper is a continuation of [5], where Lie bialgebra structures on g[u] were studied. These structures fall into different classes labelled by the vertices of the extended Dynkin diagram of g. In [5] the Lie bialgebras…
In this talk we present a division-algebra classification of the generalized supersymmetries admitting bosonic tensorial central charges. We show that for complex and quaternionic supersymmetries a whole class of compatible division-algebra…
We give a short introduction to generalized vertex algebras, using the notion of polylocal fields. We construct a generalized vertex algebra associated to a vector space h with a symmetric bilinear form. It contains as subalgebras all…
In this paper, we define and study (co)homology theories of a compatible associative algebra $A$. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures. Then we define…
We construct a generalized version for the free product of unital C*-algebras over a family of unital C*-subalgebras, starting from the group-analogue. When all the subalgebras are the same, we recover the free product with amalgamation…
This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.
We show how one may classify all semisimple algebras containing the $\mathfrak{su}(3)\oplus \mathfrak{su}(2) \oplus \mathfrak{u}(1)$ symmetry of the Standard Model and acting on some given matter sector, enabling theories beyond the…
In this paper, we give a classification of the 3-dimensional associative algebras over the complex numbers, including a construction of the moduli space, using versal deformations to determine how the space is glued together.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
Supplementary results obtained after the completion of our previous paper are given together with discussing some examples. A quick review of the previous paper is also included.
Explicit forms are given of matrix elements of generalized coherent operators based on Lie algebras su(1,1) and su(2). We also give a kind of factorization formula of the associated Laguerre polynomials.
As a generalization of singular linear spaces, we introduce the concept of t-singular linear spaces, make some anzahl formulas of subspaces, and determine the suborbits of t-singular linear groups.